(Seth Perlman/AP)

Of all the instruments government might employ to fight income inequality and reward work, the federal minimum wage, currently $7.25 per hour, is one of the bluntest.

Congress sets it based on nothing but politics. It works as a tax on business, whose benefits often accrue to middle-class teenagers, and whose costs — fewer jobs and higher prices — are partly borne by needier intended beneficiaries.

For all that, the minimum wage is popular, very popular, as voters in four red states proved once again Tuesday. Nebraskans approved a ballot measure to raise that state’s minimum wage to $8 an hour next year and $9 in 2016; South Dakotans voted to raise it to $8.50 next year. Arkansas voters approved a gradual increase to $8.50 by 2017. And Alaskans agreed to raise it to $9.75 by 2016.

In Illinois, the one blue state to consider the issue, voters opted for $10 an hour starting next year, albeit in a nonbinding referendum.

Consequently, a majority of states, containing more than half of the working-age population, have or soon will have minimum wages higher than the federal minimum.

Republican politicians, and free-market pundits like me, can complain forever about this, but the minimum wage is here to stay. All we’re accomplishing is to help fuel the controversy and thus to ensure that, whatever the minimum wage is, it will be determined the worst possible way: politically.

Minimum-wage critics need to pursue a second-best solution, which is to link the federal rate to relatively objective economic criteria and remove it from partisan conflict.

The first step would be to set a benchmark for the minimum wage based on its historical relationship to some relevant indicator. For example, since the federal government first established a definition of poverty in 1959, the average income for a full-time worker earning the minimum wage has been two-thirds of the poverty line for a family of four, an amount that nowadays is about $16,000 a year, or $8 an hour — 75 cents more than the current rate.

Alternatively, the real value of the minimum wage has oscillated around 45 percent of the average private-sector wage since its inception in 1938. That would translate to about $9 per hour today.

So let’s compromise and suggest $8.50, which would amount to an immediate $1.25-per-hour increase for minimum-wage workers in roughly half of the country.

Second, Congress could index the minimum wage to inflation, as 13 states now do. And finally, it could beef up the earned-income tax credit, a successful wage subsidy for low-income workers.

What you have just read is the outline of a grand bargain on the minimum wage. The GOP would let Democrats have at least some of the increase they have demanded for years. In return, the GOP gets political peace, because future increases would be automatic, not the subject of wrangling in Congress.

The model is the bill that Michigan’s pragmatic Republican legislature passed and its pragmatic Republican governor, Rick Snyder, signed this year. The measure increased that state’s minimum wage to $9.25 by 2018 and indexed it to inflation, thus heading off a referendum to raise it to $10.10 that unions were threatening to put on the Nov. 4 ballot.

Leading members of both parties are already on record in favor of increasing the earned-income tax credit for childless single adults, so that part of the bargain would be a win for both sides.

Who could possibly object? Democrats might complain that this deal gives them less than the $10.10 per hour President Obama has advocated, and far less than the economically risky $15 that labor activists are demanding. Still, it’s a significant raise — and, what’s more, it would be impervious to the ravages of inflation. I’d certainly like to see Obama explain a veto if the alternative is no raise at all.

Low-wage service industries and their allies on Capitol Hill might gripe that indexing the minimum wage creates permanent increases in their labor costs — and thus a strong incentive to permanently replace workers with machines. Perhaps, but surely most businesses would prefer a predictable federal minimum wage to one that fluctuates with the political winds.

I repeat: The main benefit of this grand bargain would be to end the pernicious tradition, dating to the New Deal, according to which it takes an act of Congress to increase the federal minimum wage. Let states tinker if they must; at least that level of government is closer to local market conditions. Meanwhile, national politics would be burdened by one less source of partisan conflict.

A grand bargain on the minimum wage would be pretty good for Democrats, very good for Republicans and even better for the country. Let’s see if the new majority party in Congress is smart enough to make it happen.

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